A new definition of fractional derivative

We give a new definition of fractional derivative and fractional integral. The form of the definition shows that it is the most natural definition, and the most fruitful one. The definition for 0≤α<1 coincides with the classical definitions on polynomials (up to a constant). Further, if α=1, the...

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Vydáno v:Journal of computational and applied mathematics Ročník 264; s. 65 - 70
Hlavní autoři: Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.07.2014
Témata:
Fractional derivative
Fractional integral
26A33
Fractional integral
Fractional derivative
ISSN:0377-0427, 1879-1778
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Popis
Shrnutí:We give a new definition of fractional derivative and fractional integral. The form of the definition shows that it is the most natural definition, and the most fruitful one. The definition for 0≤α<1 coincides with the classical definitions on polynomials (up to a constant). Further, if α=1, the definition coincides with the classical definition of first derivative. We give some applications to fractional differential equations.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2014.01.002